> Your code so far has bugs that I pointed out that you did not address.

I updated the code. This was not something I remembered to mention, since it didn't change the results for the zero synchrony case -- but it certainly proved your point that a difference in starting year wiped out the advantage, something I then discussed at length.

The current code (the old links should still work for this same version):

https://www.dropbox.com/s/7m8hq9yzcu5nztx/prime_reproduction...

The result:

     3 =   1963 **************************************************************
     4 =   1730 *******************************************************
     5 =   1169 *************************************
     6 =   1373 *******************************************
     7 =    831 **************************
     8 =    983 *******************************
     9 =    799 *************************
    10 =    814 **************************
    11 =    499 ***************
    12 =    842 **************************
    13 =    424 *************
    14 =    584 ******************
    15 =    563 ******************
    16 =    529 ****************
    17 =    302 *********
    18 =    553 *****************
    19 =    273 ********
    20 =    495 ***************
    21 =    400 ************
    22 =    353 ***********
    23 =    227 *******

> My corrected version shows no advantage as you'd intuitively expect.

Not so for the case my simulation models, and other assumptions produce no advantage or disadvantage (they're neutral).

> You can't assume that because something sometimes happens it always happens.

We already covered this. My simulation doesn't make that assumption, it shows the advantage that is present when that happens, however rare that might be.

> You need to take all possibilities into account evenly.

I did. That was the point of my last post. The synchronous hatch-out produces an advantage, no other circumstance does. Therefore the overall advantage is equal to the synchronous advantage multiplied by its probability. This doesn't take into account the fact that natural selection can amplify small fitness advantages, it only describes its genesis -- no feedback effects are considered.

> I have explained my point enough times that repeating it one more time is not going to cause you to see what I mean

I do see what you mean, as I explained at length in my last post. The effect being described is a factor that may explain the two cicada reproduction cycles seen in nature, as my article points out.

Dude, the code you posted again contains the exact same problem that started off this discussion! Even though I've already posted the solution! But of course that solution doesn't suit you because it shows that your previous results are wrong.

I'm not sure if you're saying here that now that you've been made aware of the problem you're just going to say that it's intentional, and that you're introducing this arbitrary assumption because that's what your simulation is supposed to investigate. If that's the case then fine, but the results of your simulation are still meaningless. The reason the prime numbers come out is still a purely synthetic artifact.

I can understand that you're bummed that your article is misleading and don't want to admit it. Just let the article be. I'm probably the first and the last person to ever notice that it's wrong. Has been very effective for psychologists ;-)

Best wishes!